It has long been known, for example through the German Patent Specification No. 317 788, to dewater and concentrate for example suspensions containing fibre by means of a substantially tubular, conically ending filter through which the suspension is fed with a screw. Apparatuses the method of working of which is based on this principle are still manufactured to a considerable extent, among others by Saffle Gjuteri & Mek. Verkstads AB and are marketed under the trade name DESICCATOR. A disadvantage of these known apparatuses, however, is that the dewatering zone does not offer the optimum flow resistance to different kinds of suspensions. Various methods of varying the flow resistance have therefore been proposed. Among others it was previously proposed through French Patent Specification No. 572 324 to vary the pressing angle and to exchange the substantially tubular, conical filter for two converging endless filter members adapted to be driven round a back and a front drive roller. This type of apparatus has been further improved, French Patent Specification No. 1 130 181, but has nevertheless not acquired any importance in comparison with dewaterers of the DESICCATOR type. One reason for this may be the circumstance that the optimum flow resistance cannot be used if this is high, because the material then tends to retreat into the thread of the feed screw.